48=3+w(2)

Solution for 48=3+w(2) equation:

48=3+w(2)

We move all terms to the left:

48-(3+w(2))=0

We add all the numbers together, and all the variables

-(+w^2+3)+48=0

We get rid of parentheses

-w^2-3+48=0

We add all the numbers together, and all the variables

-1w^2+45=0

a = -1; b = 0; c = +45;
Δ = b2-4ac
Δ = 02-4·(-1)·45
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-1}=\frac{0-6\sqrt{5}}{-2}
=-\frac{6\sqrt{5}}{-2}
=-\frac{3\sqrt{5}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-1}=\frac{0+6\sqrt{5}}{-2}
=\frac{6\sqrt{5}}{-2}
=\frac{3\sqrt{5}}{-1}
$